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Events happening on October 1, 2013

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Oct. 01, 2013 4:46am (Math 3…	Lie Theory Justin Keller (CU) X From the point of view of Frobenius algebras, we discuss how group actions can be used to coarsen the character theory of a finite dimensional semisimple Hopf algebra, when the representation ring is commutative. In particular, we show that a supercharacter table with integer entries can be constructed uniquely in such a way that it partitions the irreducible characters more finely than any other theory with integer values. Group actions and supercharacter theories
Oct. 01, 2013 4:46am (MATH 3…	Algebraic Geometry Paul Johnson (CSU) Topology and combinatorics of Hilbert schemes of points on orbifolds
Oct. 01, 2013 1pm (MATH 220)	Grad Algebra/Logic Julie Linman (CU Boulder) Reducts of Ramsey Structures, Part 3
Oct. 01, 2013 1pm (MATH 350)	Number Theory Nathan Wakefield X Consider a function \(f(n):N->N\) which measures the "growth" of the natural numbers in the following sense: for the sequence {1,2,3,....}, we define \(f(n)\) by \(f(n):=max{k in N: (n!)^2 \geq(n+k)!}\). This growth function has interesting asymptotic properties; we prove that when \(f\) is defined on the sequence of positive integers, {1,2,3,...}, we have \(\lim\limits_{n-> \infty}\frac{f(n)}{n}=1\). This idea can be generalized to any increasing sequence of integers. Specifically, we study this function defined on the sequence of prime numbers by considering the factorial like product of the sequence, and study the value of the associated limit. Comparing the growth of the prime numbers to that of the natural numbers
Oct. 01, 2013 2pm (MATH 220)	Natasha Dobrinen (DU) X The Tukey order on ultrafilters is a weakening of the well-studied Rudin-Keisler order, and the exact relationship between them is a question of interest. In a second vein, Isbell showed that there is a maximum Tukey type among ultrafilters and asked whether there are others. These two questions are the main guiding forces of the current research. In this talk, we present highlights of recent work of Blass, Dobrinen, Mijares, Milovich, Raghavan, Todorcevic, and Trujillo (in various combinations for various papers). Further information about results mentioned in this talk can be found in a recent survey article by the speaker. Survey on the structure of the Tukey theory of ultrafilters
Oct. 01, 2013 3pm (MATH 350)	PDE/Analysis Jeanne Clelland X The method of equivalence was introduced by Elie Cartan in 1908 as a procedure for finding invariants of geometric structures under the actions of pseudogroups, which most commonly appear as subgroups of the diffeomorphism group of a manifold preserving some underlying geometric structure. The method was further developed and systematized over the course of the 20th century, and it has been applied in a great variety of contexts. After briefly demonstrating Cartan’s method in the familiar context of Riemannian geometry, we will describe applications of the method of equivalence to some geometric structures related to control theory: 1. Sub-Riemannian geometry (Hughen, Moseley) and sub-Finsler geometry (C., Moseley, and Wilkens), both of which involve metrics which are defined only on a distribution on a manifold (i.e., on a subbundle of the tangent bundle of the manifold). Such metrics appear naturally in the context of optimal control of "driftless" kinematic systems. 2. Affine distributions (C., Moseley, and Wilkens), which appear naturally in the contexts of kinematic control systems with drift and dynamic control systems. 3. Dynamic equivalence of control systems (Stackpole). Dynamic equivalence generalizes the more thoroughly understood notion of static equivalence for control systems, which is addressed by the methods mentioned above. In his Ph.D. thesis, Stackpole shows how the method of equivalence may be used to address this more general notion of equivalence –- which is defined in terms of submersions rather than diffeomorphisms –- by extending to infinite prolongations. Equivalence of geometric structures in control theory via moving frames (part 1)

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